Provide an appropriate response.
-Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$ -intercepts at $( - 9,0 )$ and $( 9,0 )$ , and $y$ -intercepts at $( 0,3 )$ and $( 0 , - 3 )$ ?

Question

Provide an appropriate response.
-Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$-intercepts at $( - 9,0 )$ and $( 9,0 )$, and $y$-intercepts at $( 0,3 )$ and $( 0 , - 3 )$ ?
A) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } < 1$

B) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 9 } < 1$

C) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } > 1$

D) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 3 } < 1$

Quizplus · Accepted Answer

The equation of an ellipse centered at the origin is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ and $2b$ are the lengths of the major and minor axes, respectively. Given $x$-intercepts at $(-9,0)$ and $(9,0)$, $a = 9$, and given $y$-intercepts at $(0,3)$ and $(0,-3)$, $b = 3$. Thus, the correct inequality, representing the region inside the ellipse, is $\frac{x^2}{81} + \frac{y^2}{9} < 1$.

Provide an Appropriate Response xxx -Intercepts At (−9,0)( - 9,0 )(−9,0) And (9,0)( 9,0 )(9,0)

Provide an Appropriate Response $x$ -Intercepts At $( - 9,0 )$ And $( 9,0 )$